Re: slope of the tangent line to the curve of intersection of the vertical plane &sur

Re: slope of the tangent line to the curve of intersection of the vertical plane &sur

I am not sure exactly. This is a practice problem my teacher posed. But I am pretty sure I have to do a directional derivative since it is defined as the "slope of the tangent line to the curve formed by the intersection of z = f (x; y) and the vertical plane through a point p parallel to a unit vector u". He gave us a hint, use Du F (1,2)

edit:

So the cross product gives us < root 3, 1, 4+2*root(3)> and this is the direction of the tangent line.

So, if i make a unit vector from it and then dot it with del F, that should satisfy my above definition?

Re: slope of the tangent line to the curve of intersection of the vertical plane &sur

Re: slope of the tangent line to the curve of intersection of the vertical plane &sur

It sounds like you have already found the direction vector for the line of intersection (I didn't check your calculations, though).

HallsofIvy is right - the idea of slope in this problem makes no sense. But I'm guessing what it means is the z component of the direction vector divided by the component in the x-y plane. If so, that's easy to calculate: and , so .